The rare earth ratio of 1:1 for the alloy allows us to evaluate the electronic and phonon contributions to the observed superconductivity in fcc La\(_{0.5}\) Ce\(_{0.5}\) H\(_{10}\)  in terms of the theoretical calculations. For the consideration of the structural stability as well as the nearly constant \(T_{c}\)  behavior of the fcc LaH\(_{10}\)  phase [1]}, [2]}, [3]} at high pressures, we took the pressure of 300 GPa in the calculations. Figure 4(a) shows the electronic band structures, the total and partial electron states of density (DOS). It has been illustrated that the electronic DOS at the Fermi level [\(N(E_F\) )] in LaH\(_{10}\)  are dominated by the strong hybridization of the La 4f and H s orbitals [4]}. However, for La\(_{0.5}\) Ce\(_{0.5}\) H\(_{10}\) , the f electrons of Ce and the s electrons of H are the main compositions to \(N(E_F\) ). Therefore, the introduction of the Ce elements in the studied hydrides is mainly to reduce the phase stability pressure in terms of the chemical pre-compression from the f electrons. However, the observed superconductivity largely results from the H s electrons. In such alloy hydrides, the contributions to superconductivity from the La elements seem negligible.
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